The growing demand for autonomous cruise control and collision warning/avoidance systems has stimulated the development of frequency-modulated continuous-wave (FMCW) automotive radar. Most of the radars under development operate in the 77-GHz band, which has been reserved for these applications.
A functional block diagram of FMCW radar is depicted in FIG. 1. The system comprises a triangular waveform generator WFG 101, a voltage-controlled oscillator VCO 102 acting also as an up-converter, a coupler CPL 103, a circulator CIR 104 to provide a single-antenna operation, a transmit-receive antenna TRA 105, a quadrature mixer QMX 107, a frequency analyzer FAN 108, and a digital signal processor DSP 109.
The triangular waveform generator WFG produces a control signal CV to vary the frequency of the voltage-controlled oscillator VCO in a triangular fashion. A resulting waveform TW transmitted by the antenna TRA has a constant amplitude but its frequency sweeps the band Δf during each sweep interval TS, as depicted schematically in FIG. 2a. 
The echo RW from an obstacle OBS 106 at range R is an attenuated replica of the transmitted waveform TW, delayed in time by τ=2·R/c, where c is the speed of light. The echo RW is mixed in the quadrature mixer QMX with a portion of the transmitted waveform TW supplied by the coupler CPL. Output signals QS of the mixer QMX are analyzed in the frequency analyzer FAN to produce a beat frequency BF with the magnitude |fR| directly proportional to obstacle range
                f      R            =                    (                                                        Δ              ⁢                                                          ⁢              f                                                        T            S                          )            ⁢              (                              2            ·            R                    c                )              =                          S                    ·      τ      where |S|=|Δf|/TS is the slope of a frequency sweep.
The beat frequency fR, defined as the frequency of a reflected wave minus the frequency of an interrogating wave, is positive for frequency down-sweeps (S<0), and negative for frequency up-sweeps (S>0); hencefR=−S·τ
As known from prior art, discrimination between positive and negative beat frequencies can be accomplished when a radar system utilizes quadrature signal processing.
FIG. 2a shows schematically linear frequency variations of both the transmitted and received waveforms, and also the resulting beat frequency. As seen, the beat frequency fR has a constant magnitude except at the extremes of the sweeps (this effect is negligible in practice).
A relative movement with radial velocity V between the radar and obstacle will superimpose on the beat frequency fR a Doppler frequency shift
      f    v    =            2      ·      V        λ  where λ=c/fC is the wavelength, and fC is the carrier frequency of radar transmission. In practice, the value of Doppler shift fV is not affected by frequency modulation because the carrier frequency fC is much greater than the band Δf occupied by frequency sweeps.
For an obstacle approaching the radar with velocity V, the Doppler shift fV will be positive, whereas the shift fV will be negative for an obstacle moving away from the radar. Therefore, a measured beat frequency fB will result from two frequency components, fR and fV, suitably combined to produce a composite beat frequencyfB=fR+fV=−S·τ+fV 
It should be noted that the slope S itself can be negative (for a down-sweep) or positive (for an up-sweep).
FIG. 2b illustrates the case, in which a received waveform is delayed and Doppler-shifted with respect to a transmitted waveform.
The digital signal processor DSP uses measured beat frequency values BF, supplied by the frequency analyzer FAN, to determine both the range R and the relative velocity V of an obstacle. Estimated values of range N and velocity V are produced at output RV of the processor DSP. For correct operation, the signal processor DSP receives from the waveform generator WFG a synchronizing pulse SC indicative of the beginning and direction of each frequency sweep.
In the field of automotive radar, the main research and development effort has been concentrated on hardware demonstrations of required functionality and potential performance. However, the important problem of resistance to mutual interference has been almost neglected. It is evident now that automotive radar will become a commercial success only if the problem of resistance to multiuser interference has been solved.
It appears that conventional FM patterns and associated signal processing techniques employed in automotive radar can be severely affected by multiuser interference. Although some forms of interference can be tolerated in a properly designed system, there are others which are impossible to suppress. Consequently, conventional FM systems operating in dense-signal multiuser environment can only provide inferior obstacle detection and poor estimation of its range and velocity.
The negative effects of multiuser interference can be to some extent alleviated by utilizing irregular and non-repeating patterns of frequency modulation. For example, patent application EP 07 252 352.5 discloses an automotive radar system in which the frequency of a transmitter is varied in time in a piecewise-linear, yet non-deterministic and irregular, ‘zigzag’ fashion, so arranged as to exploit the maximum spread of allocated frequency band. The contents of patent application EP 07 252 352.5 are enclosed herein by reference.
It can be shown that the use of a randomized frequency walk can reduce the effects of mutual in-band interference caused by other users operating in the same region and sharing the same frequency band. However, efficient methods are still required which are capable of optimal processing of multi-slope FM chirp signals such as those utilized in a randomized frequency walk.
Therefore, it would be desirable to provide a method and apparatus for FM waveform design and generation that would result in improved resistance to multiuser interference, especially in automotive radar.
It would also be desirable to provide a method and apparatus for determining the range and/or velocity of a detected object in automotive radar that employs a composite multi-slope FM chirp waveform and is capable to operate in a dense-signal multiuser environment.